CN113848720B - System stability analysis method based on full-power direct-drive fan control inertia - Google Patents
System stability analysis method based on full-power direct-drive fan control inertia Download PDFInfo
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Abstract
The invention discloses a system stability analysis method based on full-power direct-driven fan control inertia, which takes single pendulum motion as an example to derive a pendulum motion equation according to a macroscopic physics theory; performing mechanical motion inertia analysis on the pendulum motion equation, and obtaining a mechanical motion inertia analysis conclusion; based on the mechanical motion inertia analysis conclusion of the pendulum bob, the inertia expression of the power electronic element is put forward, and a unified mathematical expression of a certain inertia element is deduced based on a second-order circuit of LC; deducing an inertial expression of an inner ring controller and an outer ring controller of the full-power PMSG grid-connected converter serving as a research object; the invention obtains the control stability of PMSG and the impedance Z of the AC side line l Associated with the setting of the controller and when the other conditions are unchanged, when the inner loop parameter kp 2 When the control bandwidth of the inner ring is increased, the control bandwidth of the outer ring is increased, and the outer ring parameter kp is obtained at the moment 1 The inner loop current of the PMSG converter exhibits inertial characteristics, the physical nature of which is the hysteresis effect of the feedback control.
Description
Technical Field
The invention relates to the technical field of control inertia and system stability of direct-driven fans, in particular to a system stability analysis method based on full-power direct-driven fan control inertia.
Background
With the comprehensive promotion of the policies of carbon reaching peak and carbon neutralization, china formally enters the age of rapid development of new energy. The wind power resources in China are rich, and the wind power generation device becomes an important choice for new energy power generation in the future. But the large-scale feeding of fans reduces the inertia of the system, causing oscillation problems.
At present, a full-power direct-drive fan (Permanent Magnet Synchronous Generator, PMSG) is widely adopted in a wind farm, and the fan of the type has a plurality of pairs of magnetic poles, so that a gear box is not required, and the maintenance cost is reduced. The existing researches show that various oscillation problems of the direct-drive fan are mostly caused by the change of system parameters, and the direct-drive fan belongs to oscillation instability caused by small disturbance.
In recent years, a plurality of wind power plants at home and abroad generate oscillation instability phenomena in different frequency ranges, so that huge losses are caused, and meanwhile, great challenges are brought to safe and stable operation of the system; therefore, the research on the system oscillation problem caused by the fan converter and the interaction stability of the interconnection system thereof is of great significance.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a system stability analysis method based on the control inertia of a full-power direct-drive fan, which takes a full-power PMSG grid-connected converter as a research object, deduces the inertial expression and physical meaning of an inner ring controller and an outer ring controller of the system, and simultaneously compares the inertial expression and physical meaning with a mechanical inertial motion equation to obtain a unified mathematical expression, wherein the problem that the traditional mechanical inertia is reduced and system oscillation is caused as the duty ratio of power electronic equipment in a power system is continuously increased along with the large-scale development and application of wind power resources; on the basis, a judging method of the system stability is provided by combining a control bandwidth and a Lawster criterion, and the relevance of the control parameters of the inner ring and the outer ring of the full-power fan grid-connected converter and the influence of the relevance on the fan grid-connected stability are explained according to the deduced judging expression; and then, verifying the correctness and the application range of the theoretical analysis and judgment method through PSCAD/EMTDC time domain simulation software.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
the system stability analysis method based on the full-power direct-driven fan control inertia comprises the following steps,
step (A), according to the macroscopic physics theory, a pendulum motion equation is derived from the single pendulum motion;
step (B), performing mechanical motion inertia analysis on a pendulum motion equation, and obtaining a mechanical motion inertia analysis conclusion;
step (C), based on the mechanical motion inertia analysis conclusion of the pendulum bob, the inertia expression of the power electronic element is proposed, and based on a second-order circuit of LC, a unified mathematical expression of a certain inertia element is deduced;
step (D), deducing an inertial expression of an inner ring controller and an outer ring controller of the full-power PMSG grid-connected converter serving as a research object;
comparing the inertial expression of the PMSG inner and outer ring controller with the unified mathematical expression of a certain inertial element;
step (F), a judging method of system stability is provided by combining control bandwidth and Lawster-Hercules criterion, and a judging expression is obtained;
step (G), obtaining the relevance of the control parameters of the inner ring and the outer ring of the full-power PMSG grid-connected converter and the influence of the relevance on the full-power PMSG grid-connected stability according to the judging expression;
and (H) analyzing the influence of MMC-HVDC control parameters on PMSG grid connection stability.
The system stability analysis method based on the full-power direct-drive fan control inertia comprises the steps of (A) leading out a pendulum motion equation from the single pendulum motion according to the macroscopic physics theory, wherein the single pendulum motion swings in a vertical plane, the pendulum is provided with a vertical downward gravity mg and a friction force in direct proportion to the speed, the friction coefficient is k, the pendulum motion equation is led out from the single pendulum motion and is shown as a formula (1),
wherein l represents the length of the pendulum rod, m represents the mass of the pendulum bob, the pendulum rod is hard, the mass is 0, and the included angle between the pendulum rod and the vertical line is represented by theta, v l For tangential velocity, d is the differential operator and t is the time variable.
The system stability analysis method based on the full-power direct-driven fan control inertia comprises the following steps of (B) carrying out mechanical motion inertia analysis on a pendulum motion equation and obtaining a mechanical motion inertia analysis conclusion, wherein the specific steps of carrying out mechanical motion inertia analysis on the pendulum motion equation and obtaining the mechanical motion inertia analysis conclusion are as follows,
step (B1), mechanical motion inertia analysis is carried out on a pendulum motion equation, the analysis process comprises the following specific steps,
step (B11), when the pendulum is coincident with the vertical line, d 2 θ/dt 2 =0, i.e. acceleration is 0, but dθ/dt+.0, so when passing the balance point, the inertia of the system will cause the pendulum to continue to move and deviate from the balance point;
step (B12), setting a friction coefficient k=0, wherein the pendulum bob will swing in equal amplitude with the balance point as the symmetry center, and the spectrogram of the pendulum bob shows that the pendulum bob swings in equal amplitude at a certain frequency point;
and (B2) obtaining a mechanical movement inertia analysis conclusion, wherein the mechanical movement inertia analysis conclusion is that inertia can cause the balance point of the coupling system and the balance point of the controlled state quantity X to be asynchronous, so that the system oscillates.
In the system stability analysis method based on the full-power direct-driven fan control inertia, step (C), the inertia performance of the power electronic element is proposed based on the mechanical motion inertia analysis conclusion of the pendulum, and the unified mathematical expression of a certain inertial element is deduced based on the second-order circuit of the LC, wherein the inertia performance of the proposed power electronic element is a hysteresis phenomenon with output lagging behind input, and the specific steps of deducing the unified mathematical expression of a certain inertial element based on the second-order circuit of the LC are as follows,
step (C1), a second-order circuit of the basic LC applies kirchhoff current law as shown in formula (2),
wherein L is>0，C>0, h (v) is an active circuit with v-i characteristics, i c 、i L And i is capacitance current, inductance current and port current respectively, C and L are capacitance value and inductance value respectively, d, t and s are time domain differential operator, time variable and integral variable respectively;
step (C2), integrating the time t in the formula (2), multiplying the two sides by L to obtain a new formula, as shown in the formula (3),
step (C3), the new formula can be obtained by transforming the formula (3), as shown in the formula (4),
step (C4), the unified mathematical expression of a certain inertial element can be obtained by combining the formula (3) and the formula (4), as shown in the formula (5):
wherein DeltaX is a state variable, G 1 And G 2 The coefficient of friction and the coefficient of stiffness, respectively.
The system stability analysis method based on the full-power direct-drive fan control inertia comprises the following steps of (D) deducing the inertial expression of the inner and outer ring controllers by taking a full-power PMSG grid-connected converter as a research object, wherein the PMSG is the direct-drive fan, deducing the inertial expression of the inner and outer ring controllers by taking the full-power PMSG grid-connected converter as the research object,
step (D1), according to the PMSG inner and outer ring control block diagram, when the system is in three-phase balance, obtaining a synchronous generator voltage loop equation expression under D-q axis, as shown in formula (6),
wherein omega r To synchronize the generator electrical angular velocity, ψ ds Sum phi qs Respectively a d-axis magnetic linkage and a q-axis magnetic linkage, R is a stator resistor, v ds And v qs Respectively a d-axis component and a q-axis component, i of the stator terminal voltage ds And i qs A d-axis component and a q-axis component of the stator current;
step (D2), because the resistance R.apprxeq.0 in equation (6) is negligible, then ψ ds Sum phi qs As shown in the formula (7),
wherein, psi is r For rotor flux linkage, L d And L q Respectively the d-axis inductance and the q-axis inductance of the stator, L ts And L dm Respectively a stator leakage inductance and an excitation inductance, I f Equivalent exciting current for the rotor;
step (D3), when PMSG adopts zero D-axis current control, i is present ds =0, the electromagnetic power output is shown in formula (8),
wherein P is the pole pair number, P e Is electromagnetic power, ψ r I is the rotor flux linkage s Is the stator current;
step (D4), the relation between the deviation amount of the outer loop output and the power variation amount is shown as a formula (9) according to the control block diagram of the inner loop and the outer loop of the PMSG,
wherein,,and k i1 Respectively an outer ring proportional coefficient and an integral coefficient, delta P e As the power variation, Δi sref The variable quantity of the reference value of the stator q-axis current is represented by s, which is a frequency domain differential operator;
step (D5), deriving both sides of the formula (9), as shown in the formula (10),
step (D6), combining the formula (10) with the closed loop transfer function of the MMC to obtain a new formula, as shown in the formula (11),
wherein Z is l For ac line impedance, k p2 And k i2 Respectively, inner loop proportional coefficient and integral coefficient, Δi s The current variation is PMSG;
step (D7) due to Z l ＝R+ω r L g’ And brings equation (10) into equation (11) to obtain a new equation, as shown in equation (12),
step (D8), bringing the formula (8) into the formula (12) to obtain a new formula, as shown in the formulas (13) and (14),
wherein Δi sd For d-axis current variation, G 3 And G 4 And controlling inertia coefficients and rigidity coefficients for the PMSG respectively, wherein epsilon is a self-defined coefficient.
The method for analyzing the system stability based on the full-power direct-driven fan control inertia comprises the step (E) of comparing the inertial expression of the PMSG inner and outer ring controller with the unified mathematical expression of a certain inertial element, wherein the formulas for comparison are formula (13) and formula (5).
The system stability analysis method based on the full-power direct-driven fan control inertia, step (F), the system stability judgment method is provided by combining the control bandwidth and the Lawster-Hertzian criterion, and a judgment expression is obtained, the specific steps of obtaining the judgment expression are as follows,
step (F1), according to the Lawster-Hercules criterion, the coefficient in formula (14) satisfies the condition G 3 >0, and G 4 >The system is stable at 0, so that the criterion can be obtained as shown in formula (15),
in the step (F2), the automatic control principle can know that the PI parameter of the PSMG converter can generally satisfy the molecular of formula (15) being greater than 0, as shown in formula (16),
the system stability analysis method based on the full-power direct-driven fan control inertia, step (G), the relevance of the control parameters of the inner ring and the outer ring of the full-power PMSG grid-connected converter and the influence of the relevance on the full-power PMSG grid-connected stability are obtained according to the judging expression, the specific steps are as follows,
step (G1), the relevance of the control parameters of the inner ring and the outer ring of the full-power PMSG grid-connected converter is that the control stability of the PMSG and the line impedance Z of the alternating current side l Correlating with a setting value of the controller;
step (G2), the influence on the grid-connected stability of the full-power PMSG is that when other conditions are unchanged, the inner loop parameter k is p2 When the inner loop control bandwidth is increased, the outer loop parameter k is increased p1 Such that equation (16) can estimate the stability domain of the system with respect to the outer loop control parameters based on the inner loop control parameters of the PMSG.
According to the system stability analysis method based on the full-power direct-driven fan control inertia, the step (H) is used for analyzing the influence of MMC-HVDC control parameters on PMSG grid-connected stability, the analysis method is that an MMC model is built in PSCAD/EMTDC and simulated, so that the accuracy of a formula (16) is verified, the MMC model is built and simulated based on a control variable method, other parameter values are kept unchanged, and the change is carried outAnd (3) observing the change of the dominant characteristic root and the power output of the system, and judging the stability of the system.
The beneficial effects of the invention are as follows: according to the system stability analysis method based on the full-power direct-driven fan control inertia, firstly, a full-power PMSG grid-connected converter is taken as a research object, the inertia expression and the physical meaning of an inner ring controller and an outer ring controller of the full-power PMSG grid-connected converter are deduced, and meanwhile, the full-power PMSG grid-connected converter is compared with a mechanical inertia motion equation to obtain a unified mathematical expression; on the basis, a judging method of the system stability is provided by combining a control bandwidth and a Lawster criterion, and the relevance of the control parameters of the inner ring and the outer ring of the full-power fan grid-connected converter and the influence of the relevance on the fan grid-connected stability are explained according to the deduced judging expression; the accuracy and the application range of the theoretical analysis and judgment method are verified through PSCAD/EMTDC time domain simulation software; the control stability of PMSG and the AC side line impedance Z are obtained by the analysis method l Associated with the setting of the controller and when the other conditions are unchanged, when the inner loop parameter kp 2 When the control bandwidth of the inner ring is increased, the control bandwidth of the outer ring is increased, and the outer ring parameter kp is obtained at the moment 1 The stability threshold of the PMSG converter is reduced, and the inner loop current of the PMSG converter shows inertial characteristics due to the influence of factors such as inductance elements, submodule capacitance and control hysteresis in a circuit, and provides a possible oscillation mode for the system, the physical essence of the PMSG converter is hysteresis effect of feedback control, and the accuracy of theoretical analysis and judgment expression is verified through PSCAD/EMTDC time domain simulation.
Drawings
FIG. 1 is a diagram of pendulum motion characteristics of a system stability analysis method based on full power direct drive fan control inertia of the present invention;
FIG. 2 is a schematic diagram of an LC tank circuit of the present invention;
FIG. 3 is a block diagram of the PMSG inner and outer loop control of the present invention;
FIG. 4 is a vector diagram of a PMSG employing ZDC control according to the present invention;
FIG. 5 is a schematic diagram of PMSG parameter set versus stability according to the present invention;
FIG. 6 is a schematic representation of the stability domains of the present invention.
Detailed Description
The invention will be further described with reference to the drawings.
As shown in fig. 1, the system stability analysis method based on the full-power direct-drive fan control inertia of the invention comprises the following steps,
step (A) of deriving a pendulum motion equation by taking the single pendulum motion of FIG. 1 as an example according to the macroscopic physics theory, wherein the single pendulum motion swings in a vertical plane, the pendulum is set to bear a vertical downward gravity mg and a friction force proportional to the speed, the friction coefficient is k, the pendulum motion equation is derived from the single pendulum motion and is shown as a formula (1),
wherein l represents the length of the pendulum rod, m represents the mass of the pendulum bob, the pendulum rod is hard, the mass is 0, and the included angle between the pendulum rod and the vertical line is represented by theta, v l For tangential velocity, d is the differential operator and t is the time variable.
Step (B), carrying out mechanical motion inertia analysis on the pendulum motion equation and obtaining a mechanical motion inertia analysis conclusion, wherein the specific steps of carrying out mechanical motion inertia analysis on the pendulum motion equation and obtaining the mechanical motion inertia analysis conclusion are as follows,
step (B1), mechanical motion inertia analysis is carried out on a pendulum motion equation, the analysis process comprises the following specific steps,
step (B11), when the pendulum is coincident with the vertical line, d 2 θ/dt 2 =0, i.e. acceleration is 0, but dθ/dt+.0, so when passing the balance point, the inertia of the system will cause the pendulum to continue to move and deviate from the balance point;
step (B12), setting a friction coefficient k=0, wherein the pendulum bob will swing in equal amplitude with the balance point as the symmetry center, and the spectrogram of the pendulum bob shows that the pendulum bob swings in equal amplitude at a certain frequency point;
and (B2) obtaining a mechanical movement inertia analysis conclusion, wherein the mechanical movement inertia analysis conclusion is that inertia can cause the balance point of the coupling system and the balance point of the controlled state quantity X to be asynchronous, so that the system oscillates.
Step (C), based on the mechanical motion inertia analysis conclusion of the pendulum bob, the inertia expression of the power electronic element is proposed, and a unified mathematical expression of a certain inertia element is deduced based on a second-order circuit of the LC, wherein the inertia expression of the proposed power electronic element is represented as a hysteresis phenomenon that the output lags the input, for example, an inductance element has magnetic field inertia, so that the current lags by a voltage pi/2; the capacitive element has an electric field inertia, resulting in a voltage hysteresis current pi/2, thus in the vicinity of a certain equilibrium point of the system, the currentBut->Thereby inducing electromagnetic oscillation; whereas the specific steps for deriving a unified mathematical expression of an inertial element by an LC-based second-order circuit (as shown in figure 2) are as follows,
step (C1), a second-order circuit of the basic LC applies kirchhoff current law as shown in formula (2),
wherein L is>0，C>0, h (v) is an active circuit with v-i characteristics, i c 、i L And i is capacitance current, inductance current and port current respectively, C and L are capacitance value and inductance value respectively, d, t and s are time domain differential operator, time variable and integral variable respectively;
step (C2), integrating the time t in the formula (2), multiplying the two sides by L to obtain a new formula, as shown in the formula (3),
step (C3), the new formula can be obtained by transforming the formula (3), as shown in the formula (4),
step (C4), the unified mathematical expression of a certain inertial element can be obtained by combining the formula (3) and the formula (4), as shown in the formula (5):
wherein DeltaX is a state variable, G 1 And G 2 The coefficient of friction and the coefficient of stiffness, respectively.
Equation (5) describes the rate of change of the speed of a state variable Δx, the speed and its own coupling relationship, so the solution of this equation reflects the dynamic response of the state variable Δx at the equilibrium point, as well as the inertia and damping characteristics of the system.
Step (D), deducing an inertial expression of an inner ring controller and an outer ring controller of the full-power PMSG grid-connected converter by taking the full-power PMSG grid-connected converter as a research object, wherein the PMSG is a direct-drive fan, the inner ring current of the PMSG converter shows inertial characteristics due to the influence of factors such as inductance elements, submodule capacitance, control hysteresis and the like in a circuit, a possible oscillation mode is provided for a system, the physical essence of the system is hysteresis effect of feedback control, the full-power PMSG grid-connected converter is taken as the research object to deduce the inertial expression of the inner ring controller and the outer ring controller of the full-power PMSG grid-connected converter, and the specific steps are as follows,
step (D1), according to a PMSG inner and outer ring control block diagram (shown in figure 3), when the system is balanced in three phases, a synchronous generator voltage loop equation expression under D-q axis is obtained, as shown in a formula (6),
wherein omega r Is the same asElectric angular velocity of step generator, ψ ds Sum phi qs Respectively a d-axis magnetic linkage and a q-axis magnetic linkage, R is a stator resistor, v ds And v qs Respectively a d-axis component and a q-axis component, i of the stator terminal voltage ds And i qs A d-axis component and a q-axis component of the stator current;
step (D2), because the resistance R.apprxeq.0 in equation (6) is negligible, then ψ ds Sum phi qs As shown in the formula (7),
wherein, psi is r For rotor flux linkage, L d And L q Respectively the d-axis inductance and the q-axis inductance of the stator, L ts And L dm Respectively a stator leakage inductance and an excitation inductance, I f Equivalent exciting current for the rotor;
cross-coupling terms of d-axis and q-axis are under study Δv s And Δi s Can be regarded as disturbance and mathematically compensated in the control strategy;
step (D3), when PMSG adopts zero D-axis current control, i is present ds =0, the electromagnetic power output is shown in formula (8),
wherein P is the pole pair number, P e Is electromagnetic power, ψ r I is the rotor flux linkage s Is the stator current;
step (D4), the relation between the deviation amount of the outer loop output and the power variation amount is shown as a formula (9) according to the control block diagram of the inner loop and the outer loop of the PMSG,
wherein k is p1 And k i1 Respectively an outer ring proportional coefficient and an integral coefficient, delta P e As the power variation, Δi sref The variable quantity of the reference value of the stator q-axis current is represented by s, which is a frequency domain differential operator;
step (D5), deriving both sides of the formula (9), as shown in the formula (10),
step (D6), combining the formula (10) with the closed loop transfer function of the MMC to obtain a new formula, as shown in the formula (11),
wherein Z is l For ac line impedance, k p2 And k i2 Respectively, inner loop proportional coefficient and integral coefficient, Δi s The current variation is PMSG;
step (D7) due to Z l ＝R+ω r L g And brings equation (10) into equation (11) to obtain a new equation, as shown in equation (12),
step (D8), bringing the formula (8) into the formula (12) to obtain a new formula, as shown in the formulas (13) and (14),
wherein Δi sd For d-axis current variation, G 3 And G 4 And controlling inertia coefficients and rigidity coefficients for the PMSG respectively, wherein epsilon is a self-defined coefficient.
Comparing the inertial expression of the PMSG inner and outer ring controllers with the unified mathematical expression of a certain inertial element, wherein the formulas for comparison are formula (13) and formula (5);
wherein, as can be seen from comparing the formula (5) and the formula (13), the output quantity Deltai of PMSG converter control s The inertial equation under the damping effect is satisfied; due to the influence of factors such as line inductance, submodule capacitance, control hysteresis and the like, the current of the PMSG controller shows inertial characteristics and provides a possible oscillation mode for the system; as can be seen from the control block diagram, the inertia exhibited by the PMSG converter is mathematically represented as being generated by the integral of the PI controller, and the physical nature of the inertia is a hysteresis effect of feedback control; because the conversion speed of the input quantity and the response speed of the control are not synchronous, certain deviation can be generated during actual output, and the deviation signal of the controller cannot be completely converted into control action in time, and the hysteresis effect can be called the inertia of the controller; from analysis, this hysteresis effect is 2-order, so that the PMSG control output characteristics substantially conform to equation (14); the stability definition in the automatic control theory is that after a certain state variable X is disturbed, if the motion characteristic of the state variable is bounded and converged, the system is stable; otherwise, if the motion characteristic of the state variable is unbounded or diverged, the system is unstable; if bounded but not converged to critical stability.
Step (F), a judging method of the system stability is provided by combining the control bandwidth and the Lawster-Herculez criterion, a judging expression is obtained, the specific steps for obtaining the judging expression are as follows,
step (F1), according to the Lawster-Hercules criterion, the coefficient in formula (14) satisfies the condition G 3 >0, and G 4 >The system is stable at 0, so that the criterion can be obtained as shown in formula (15),
in the step (F2), the automatic control principle can know that the PI parameter of the PSMG converter can generally satisfy the molecular of formula (15) being greater than 0, as shown in formula (16),
step (G), obtaining the relevance of the control parameters of the inner ring and the outer ring of the full-power PMSG grid-connected converter and the influence of the relevance on the grid-connected stability of the full-power PMSG according to a judging expression, wherein the specific steps are as follows,
step (G1), the relevance of the control parameters of the inner ring and the outer ring of the full-power PMSG grid-connected converter is that the control stability of the PMSG and the line impedance Z of the alternating current side l Correlating with a setting value of the controller;
step (G2), the influence on the grid-connected stability of the full-power PMSG is that when other conditions are unchanged, the inner loop parameter k is p2 When the inner loop control bandwidth is increased, the outer loop parameter k is increased p1 Such that equation (16) can estimate the stability domain of the system with respect to the outer loop control parameters based on the inner loop control parameters of the PMSG.
The step (H) is based on the analysis of the influence of MMC-HVDC control parameters on PMSG grid-connected stability, the analysis method is to build an MMC model in PSCAD/EMTDC and simulate, thereby verifying the accuracy of a formula (16), and the MMC model is built and simulate based on a control variable method, keeping other parameter values unchanged and changing k p1 And (3) observing the change of the dominant characteristic root and the power output of the system, and judging the stability of the system.
Table 1MMC outer loop control operating parameters
As can be seen from table 1, in table 1, B represents the calculated stability boundary value. Lambda (lambda) i Is the dominant feature root closest to the virtual axis calculated in the full-order model, and changes in 2 seconds in the simulation processOf the active power curve change characteristicsAs shown in fig. 5; when k is 1 When the value is 0.471, the system is in a stable running state; let k 1 =0.786, when the system oscillates with constant amplitude, in a critical steady state; further increase k 1 By observing the power curve, the system diverges and is unstable.
The same conclusion can be drawn by analyzing the dominant feature root of the system in Table 2, with k following 1 Increasing, the real part of the dominant feature root of the system decreases, when k 1 When the threshold value B is exceeded, the real part of the dominant feature root is larger than 0, and the system is unstable; in summary, the simulation results of fig. 5 are consistent with the calculation results in table 1, so the validity of equation (16) can be demonstrated.
The following describes the use effect of the system stability analysis method based on the control inertia of the full-power direct-drive fan,
as can be seen from fig. 6, a hatched area a in the figure indicates a parameter setting range in which the system can stably operate when other parameters are unchanged; region B represents the unstable region of the system, the main reason for the instability is k 2 The value of (2) is set too large;
when designing PMSG control parameters, generally, the control bandwidth of the inner ring is firstly determined, then the control bandwidth of the outer ring and related parameters are set according to the bandwidth and parameters of the inner ring, the related expression is shown in formula (17),
wherein omega i ＝2πf i ，f i Controlling bandwidth for an inner loop of the PMSG; zeta type toy i Is the damping ratio; v (V) dc Is a direct-current side voltage value; k (k) i And T i Setting a reference value for an outer ring parameter calculated according to an inner ring control bandwidth, wherein in the simulation process, the range of the inner ring bandwidth is set as follows: 50-280 Hz.
In summary, the invention takes the full-power PMSG grid-connected converter as a research object to deduce the inertial expression and physical meaning of the inner and outer ring controllers thereof, and meanwhile, the invention is compared with a mechanical inertial motion equation to obtain a unified mathematical expressionThe method comprises the steps of carrying out a first treatment on the surface of the On the basis, a judging method of the system stability is provided by combining a control bandwidth and a Lawster criterion, and the relevance of the control parameters of the inner ring and the outer ring of the full-power fan grid-connected converter and the influence of the relevance on the fan grid-connected stability are explained according to the deduced judging expression; the accuracy and the application range of the theoretical analysis and judgment method are verified through PSCAD/EMTDC time domain simulation software; the control stability of PMSG and the AC side line impedance Z are obtained by the analysis method l Associated with the setting of the controller and when the other conditions are unchanged, when the inner loop parameter kp 2 When the control bandwidth of the inner ring is increased, the control bandwidth of the outer ring is increased, and the outer ring parameter kp is obtained at the moment 1 The stability threshold of the PMSG converter is reduced, and the inner loop current of the PMSG converter shows inertial characteristics due to the influence of factors such as inductance elements, submodule capacitance and control hysteresis in a circuit, and provides a possible oscillation mode for the system, the physical essence of the PMSG converter is hysteresis effect of feedback control, and the accuracy of theoretical analysis and judgment expression is verified through PSCAD/EMTDC time domain simulation.
The foregoing has outlined and described the basic principles, features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (5)
1. A system stability analysis method based on full-power direct-driven fan control inertia is characterized by comprising the following steps: comprises the steps of,
step (A), according to the macroscopic physics theory, a pendulum motion equation is derived from the single pendulum motion;
step (B), performing mechanical motion inertia analysis on a pendulum motion equation, and obtaining a mechanical motion inertia analysis conclusion;
a step (C) of providing the inertial representation of the power electronic component based on the analysis conclusion of the mechanical motion inertia of the pendulum, and deriving a unified mathematical expression of a certain inertial component based on the second-order circuit of the LC, wherein the provided inertial representation of the power electronic component is a hysteresis with output lagging behind input, and the specific steps of deriving the unified mathematical expression of a certain inertial component based on the second-order circuit of the LC are as follows,
step (C1), a second-order circuit of the basic LC applies kirchhoff current law as shown in formula (2),
wherein L is>0，C>0, h (v) is an active circuit with v-i characteristics, i c 、i L And i is capacitance current, inductance current and port current respectively, C and L are capacitance value and inductance value respectively, d, t and s are time domain differential operator, time variable and integral variable respectively;
step (C2), integrating the time t in the formula (2), multiplying the two sides by L to obtain a new formula, as shown in the formula (3),
step (C3), the new formula can be obtained by transforming the formula (3), as shown in the formula (4),
step (C4), the unified mathematical expression of a certain inertial element can be obtained by combining the formula (3) and the formula (4), as shown in the formula (5):
wherein DeltaX is a state variable, G 1 And G 2 The friction coefficient and the rigidity coefficient are respectively;
step (D), deducing the inertial expression of the inner and outer ring controllers by taking the full-power PMSG grid-connected converter as a research object, wherein the PMSG is a direct-drive fan, deducing the inertial expression of the inner and outer ring controllers by taking the full-power PMSG grid-connected converter as the research object as follows,
step (D1), according to the PMSG inner and outer ring control block diagram, when the system is in three-phase balance, obtaining a synchronous generator voltage loop equation expression under D-q axis, as shown in formula (6),
wherein omega r To synchronize the generator electrical angular velocity, ψ ds Sum phi qs Respectively a d-axis magnetic linkage and a q-axis magnetic linkage, R is a stator resistor, v ds And v qs Respectively a d-axis component and a q-axis component, i of the stator terminal voltage ds And i qs A d-axis component and a q-axis component of the stator current;
step (D2), because the resistance R.apprxeq.0 in equation (6) is negligible, then ψ ds Sum phi qs As shown in the formula (7),
wherein, psi is r For rotor flux linkage, L d And L q Respectively the d-axis inductance and the q-axis inductance of the stator, L ts And L dm Respectively a stator leakage inductance and an excitation inductance, I f Equivalent exciting current for the rotor;
step (D3), when PMSG adopts zero D-axis current control, i is present ds =0, the electromagnetic power output is shown in formula (8),
wherein P is the pole pair number, P e Is electromagnetic power, ψ r I is the rotor flux linkage s Is the stator current;
step (D4), the relation between the deviation amount of the outer loop output and the power variation amount is shown as a formula (9) according to the control block diagram of the inner loop and the outer loop of the PMSG,
wherein k is p1 And k i1 Respectively an outer ring proportional coefficient and an integral coefficient, delta P e As the power variation, Δi sref The variable quantity of the reference value of the stator q-axis current is represented by s, which is a frequency domain differential operator;
step (D5), deriving both sides of the formula (9), as shown in the formula (10),
step (D6), combining the formula (10) with the closed loop transfer function of the MMC to obtain a new formula, as shown in the formula (11),
wherein Z is l For ac line impedance, k p2 And k i2 Respectively, inner loop proportional coefficient and integral coefficient, Δi s The current variation is PMSG;
step (D7) due to Z l ＝R+ω r L g And brings equation (10) into equation (11) to obtain a new equation, as shown in equation (12),
step (D8), bringing the formula (8) into the formula (12) to obtain a new formula, as shown in the formulas (13) and (14),
wherein Δi sd For d-axis current variation, G 3 And G 4 Controlling inertia coefficient and rigidity coefficient for PMSG, epsilon being self-defining coefficient;
comparing the inertial expression of the PMSG inner and outer ring controllers with the unified mathematical expression of a certain inertial element, wherein the formulas for comparison are formula (13) and formula (5);
step (F), a judging method of the system stability is provided by combining the control bandwidth and the Lawster-Herculez criterion, and a judging expression is obtained, wherein the specific steps for obtaining the judging expression are as follows,
step (F1), according to the Lawster-Hercules criterion, the coefficient in formula (14) satisfies the condition G 3 >0, and G 4 >The system is stable at 0, so that the criterion can be obtained as shown in formula (15),
in the step (F2), the automatic control principle can know that the PI parameter of the PSMG converter can generally satisfy the molecular of formula (15) being greater than 0, as shown in formula (16),
step (G), obtaining the relevance of the control parameters of the inner ring and the outer ring of the full-power PMSG grid-connected converter and the influence of the relevance on the full-power PMSG grid-connected stability according to the judging expression;
and (H) analyzing the influence of MMC-HVDC control parameters on PMSG grid connection stability.
2. The system stability analysis method based on the full-power direct-drive fan control inertia of claim 1, wherein the system stability analysis method is characterized by comprising the following steps of: step (A) of deriving a pendulum motion equation from a single pendulum motion according to a macroscopic physics theory, wherein the single pendulum motion swings in a vertical plane, the pendulum is provided to receive a gravity mg vertically downward and a friction force in direct proportion to a speed, the friction coefficient is k, the pendulum motion equation is derived from the single pendulum motion as shown in formula (1),
wherein l represents the length of the pendulum rod, m represents the mass of the pendulum bob, the pendulum rod is hard, the mass is 0, and the included angle between the pendulum rod and the vertical line is represented by theta, v l For tangential velocity, d is the differential operator and t is the time variable.
3. The system stability analysis method based on the full-power direct-drive fan control inertia of claim 2, wherein the system stability analysis method is characterized by comprising the following steps of: step (B), carrying out mechanical motion inertia analysis on the pendulum motion equation and obtaining a mechanical motion inertia analysis conclusion, wherein the specific steps of carrying out mechanical motion inertia analysis on the pendulum motion equation and obtaining the mechanical motion inertia analysis conclusion are as follows,
step (B1), mechanical motion inertia analysis is carried out on a pendulum motion equation, the analysis process comprises the following specific steps,
step (B11), when the pendulum is coincident with the vertical line, d 2 θ/dt 2 =0, i.e. acceleration is 0, but dθ/dt+.0, so when passing the balance point, the inertia of the system will cause the pendulum to continue to move and deviate from the balance point;
step (B12), setting a friction coefficient k=0, wherein the pendulum bob will swing in equal amplitude with the balance point as the symmetry center, and the spectrogram of the pendulum bob shows that the pendulum bob swings in equal amplitude at a certain frequency point;
and (B2) obtaining a mechanical movement inertia analysis conclusion, wherein the mechanical movement inertia analysis conclusion is that inertia can cause the balance point of the coupling system and the balance point of the controlled state quantity X to be asynchronous, so that the system oscillates.
4. The system stability analysis method based on the full-power direct-drive fan control inertia of claim 1, wherein the system stability analysis method is characterized by comprising the following steps of: step (G), obtaining the relevance of the control parameters of the inner ring and the outer ring of the full-power PMSG grid-connected converter and the influence of the relevance on the grid-connected stability of the full-power PMSG according to a judging expression, wherein the specific steps are as follows,
step (G1), the relevance of the control parameters of the inner ring and the outer ring of the full-power PMSG grid-connected converter is that the control stability of the PMSG and the line impedance Z of the alternating current side l Correlating with a setting value of the controller;
step (G2), the influence on the grid-connected stability of the full-power PMSG is that when other conditions are unchanged, the inner loop parameter k is p2 When the inner loop control bandwidth is increased, the outer loop parameter k is increased p1 Such that equation (16) can estimate the stability domain of the system with respect to the outer loop control parameters based on the inner loop control parameters of the PMSG.
5. The system stability analysis method based on the full-power direct-drive fan control inertia of claim 4, wherein the system stability analysis method is characterized by comprising the following steps of: the step (H) is based on the analysis of the influence of MMC-HVDC control parameters on PMSG grid-connected stability, the analysis method is to build an MMC model in PSCAD/EMTDC and simulate, thereby verifying the accuracy of a formula (16), and the MMC model is built and simulate based on a control variable method, keeping other parameter values unchanged and changing k p1 And (3) observing the change of the dominant characteristic root and the power output of the system, and judging the stability of the system.
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